TY - JOUR
T1 - Consistent Forcing Scheme in the Simplified Lattice Boltzmann Method for Incompressible Flows
AU - Gao , Yuan
AU - Yang , Liuming
AU - Yu , Yang
AU - Hou , Guoxiang
AU - Hou , Zhongbao
JO - Communications in Computational Physics
VL - 5
SP - 1427
EP - 1452
PY - 2021
DA - 2021/10
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2021-0058
UR - https://global-sci.org/intro/article_detail/cicp/19935.html
KW - Simplified lattice Boltzmann method, force term implementation, non-uniform body force, ChapmanEnskog analysis, the discrete effect.
AB - <p style="text-align: justify;">Considering the fact that the lattice discrete effects are neglected while introducing a body force into the simplified lattice Boltzmann method (SLBM), we propose
a consistent forcing scheme in SLBM for incompressible flows with external forces. The
lattice discrete effects are considered at the level of distribution functions in the present
forcing scheme. Consequently, it is more accurate compared with the original forcing
scheme used in SLBM. Through Taylor series expansion and Chapman-Enskog (CE)
expansion analysis, the present forcing scheme can be proven to recover the macroscopic Navier-Stokes (N-S) equations. Then, the macroscopic equations are resolved
through a fractional step technique. Furthermore, the material derivative term is discretized by the central difference method. To verify the results of the present scheme,
we simulate with multiple forms of external force interactions including the space- and
time-dependent body forces. Hence, the present forcing scheme overcomes the disadvantages of the original forcing scheme and the body force can be accurately imposed
in the present scheme even when a coarse mesh is applied while the original scheme
fails. Excellent agreements between the analytical solutions and our numerical results
can be observed.</p>